## Nonlinear mappings of monotone type |

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### Contents

Convex analysis | 18 |

Related topics and exercises | 31 |

Sobolev spaces | 44 |

Copyright | |

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### Common terms and phrases

angle-bounded assume assumptions bounded domain bounded sets boundedness Brezis Browder coercive compact operator consider continuous function contradicts convergence convex function convex l.s.c. function convex set deduce defined demicontinuous denote domain in RN dual space duality map element equivalent exists a constant exists a sequence finite follows Hammerstein equations Hence Hilbert space implies integral lemma Let Q lim inf lim sup linear monotone linear operator locally bounded mapping of type maximal monotone mapping monotone operator Moreover Nemitskyi operator norm obtain problem proper convex l.s.c. Proposition Let prove pseudo-monotone operator pseudo-monotone property quasi-bounded reflexive Banach space single-valued Sobolev spaces space and let strictly convex subdifferential Suppose surjective Theorem Let Txux type S+ variational inequality variational solution weak topology weakly x e Q